Answer
Because the slopes of the two lines are the same, we see that they are parallel.
Work Step by Step
To do this, we must prove that the slopes are the same.
Finding the slope of the third side of the triangle is simple:
$ m=\frac{2c-0}{2b-0}=c/b$
We use the midpoint formula to find the points in the middle of each other side of the triangle:
$ (\frac{2a+2b}{2}, \frac{2c+0}{2})$
$ (a+b,c)$
And for the other side:
$ (\frac{2a+0}{2}, \frac{0+0}{2})$
$({a,0})$
We now use the slope formula for these two midpoints:
$ \frac{c-0}{(a+b)-a}$
$m = c/b$
Because the slopes of the two lines are the same, we see that they are parallel.
